This document contains 10 questions related to work, energy and power concepts in mechanics. Question 1 asks about calculating the work done to bring a moving train to rest. Question 2 asks about calculating the impulse and average force exerted on a ball hit by a bat. Question 3 asks about calculating the compression of a spring when a moving train strikes a bumper and stops.

1. Tutorial Sheet 09
Unit 5: Work Energy and Power
Q1 A train is moving along a track whose gradient is 1 in 100. The weight of train is 6000 kN. To avoid an
accident, the train is brought to rest applying brakes in 250 m length along the track. The resistance due to
friction and air motion is 15 N per kN weight of train. Find the work done in bringing the train to rest.
Q2 A ball of mass 250 g is moving with a velocity of 15 m/s is hit by a bat so that ball is turned back with a
velocity of 25 m/s. The duration of contact between the ball and the bat is 0.02 s. Find the impulse and the
average force exerted on the ball by the bat.
Q3 A train weighing 50 ton is slides down 30 m along the inclined tracks as shown in figure. When the train
comes down at Q and strikes the bumper and stops, find the compression of the spring. Assuming the
frictional resistance 4/985th
of the weight of train, if the stiffness of the spring is 13.5 kN/mm
Q4 A bullet of mass 50 g is fired horizontally into a body of mass 12 kg which is suspended by the string of
length 1m. Due to this impact, the body swings through an angle of 30° with the vertical. Determine the
velocity of the bullet at impact.
Q5 A cricket ball of mass 250 g weighing 235 g is sliding down a horizontal smooth cylinder of radius 15 cm,
from top point A as shown in figure. Calculate the reaction exerted by the cylinder on ball at position B,
defined angle Φ = 25°. Also determine position, when the ball will leave the surface and corresponding
velocity.
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2. Tutorial Sheet 09
Q6 Two masses of 750 kg and 550 kg are attached at the ends of the rope. The rope passes over a pulley of 90
cm diameter. The mass of pulley is 120 kg and its radius of gyration is 45 cm about its axis of rotation.
Determine the torque applied on the pulley to raise the mass of 750 kg with an acceleration of 1.5 m/s2
.
Neglect the weight of rope and friction between rope and pulley.
Q7 A force F = 2.5 t Newton, where t is in seconds acts on a mass of 300 kg initially at rest for a period of 30
seconds. Calculate (i) the impulse on the mass (ii) the velocity of the mass (iii) average force which should
have resulted in same velocity
Q8 A pile driver of mass 350 kg falls from a height of 4m on a pile of mass 1500 kg. the pile is driven 0.3 m into
the ground. Find the common velocity of pile and driver after the impact and average resistance of the
ground to the penetration of pile.
Q9 The two orbital maneuvering engines of the space shuttle developed 26kN of thrust each. If the shuttle if
travelling in orbit at a speed of 28000 km/h, how long would it take to reach a speed of 28100 km/h after the
two engines are fired? The Mass of shuttle of 90000 kg.
Q10(i) State and prove law of conservation of energy.
(ii) What is work energy theorem?
(ii) What is meant by the term Energy? Explain various types of mechanical energies?
Answers:
(1) w = 37500 kN –m
(2) F= -500 N
(3) k = 60.8 mm
(4) v = 390.42 m/s
(5) v = 0.99 m/s
(6) Torque = 1841 N-m
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3. Tutorial Sheet 09
(7) (i) 1125 N-s (ii) 3.75 m/s (iii) Avg force = 37.5 N
(8) V = 1.67 m/s ; R = 26747.3 N
(9) t = 48 s
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